Henry Rzepa's Blog

One of the important aspects of chemical reaction mechanisms is the order in which things happen. More specifically, the order in which bonds make or break when there are more than two involved in undertaking a reaction. So we have:

1. concerted mechanisms, when all bonds in any particular stage of a mechanism are changing in concert via a unique transition state,
2. asynchronous concerted mechanism, when all the bonds are changing, but not necessarily all at the same rate and which may involve so called “hidden intermediates”, but which nevertheless stil involves only one transition state.
3. stepwise mechanisms, in which more than one transition state is involved, connected by a discrete intermediate along the pathway.

Here I consider an example of another type of (isomerisation) mechanism, involving bond rotations rather than bond formations or breakages. The two bonds in this case have a higher bond order than 1, and so are starting to verge on a type of isomerism known as atropisomerism, where the rotation takes place on a relatively slow time scale (unlike single bonds themselves, where rotation about them is normally relatively fast). Do two such bonds rotate in a stepwise or a concerted manner? In the structure below, we have two rotatable bonds, shown in red and blue, which due to conjugation of the lone electron pair on the nitrogen atoms with the carbonyl group have bond orders >1. Do these bonds rotate in concert or in a stepwise manner?

The calculations of the rotations are done at the B3LYP+GD3+BJ/Def2-SVPP/SCRF=DCM level, Data DOI: 10.14469/hpc/12299

1. Firstly, for the system R=R’ = Me. The reaction coordinate is specified around the red bond.
   

   The animation along the IRC (Intrinsic reaction coordinate) appears below, where you can see the red bond rotating and the blue bond spectating.
   

2. The response of the dihedral angles about both bonds is shown below, which reinforces the conclusion that whilst one dihedral changes by about 180°, the other hardly changes. The overall dipole moment changes significantly as a result of the relative orientation of the two carbonyl groups changing. The two bonds can be said to rotate in a stepwise mechanism, involving an intermediate where one has rotated and the other has not.
   
   
   
3. When the bulk of the central group is increased, different behaviour is now observed.
   
   
4. Both dihedral angles now change by ~180°, in concert but not in synchrony! The first more or less transforms evenly by ~180°, but the second changes direction at ~IRC=-5 to rejoin the other.
   
   

When the steric bulk means that the rotating substituents start to interfere with each other, so-called “gearing” starts to take place where the motions of the two become coupled by the gears. The rotations are now a concerted asynchronous process.

So now to my concluding thought. The above is a simple example of gearing involving rotation about two coupled bonds. So how many bonds can be simultaneously geared so that when one rotates, the others do as well? I am now hunting for an example of three such bonds geared together. And is there a limit to how many can do so in concert? Here we enter into analogy with bond cleavage, where there are numerous examples of bonds breaking in concert, if not in synchrony. Most pericyclic processes are of this type. Is there a similar patten in bond rotations?